Harmonics and Waveforms

Salutations again synth seekers! Last time, we discussed the nature of oscillation and, in turn, oscillators. These controlled oscillations in voltage are translated into definable pitch and sound: slower oscillations result in lower pitches while faster ones yield higher pitches. And if you combine different oscillators, you’ll wind up with multiple notes at once (AKA a chord).

While having actual notes to use is a key staring point, it’d be nice to be able to mold and sculpt these pitches/oscillators as we see fit. Do we want something bright and brash? Or perhaps soft and mellow? Perhaps something hollow and mysterious?

To achieve these different tones/timbres, one of the first variables to adjust is the waveform of each oscillator. We’ll discuss four (technically five) basic waveforms today, but to understand waveforms, you first need to know a little bit about harmonics.

Harmonics are a science unto themselves, so if you really want to dive deep, click here to go wild with math, graphs, etc. For everyone else, I just want to touch on the basics, so you’ll feel more comfortable with the world of waveforms.

In the most basic sense, harmonics are the means by which we create different pitches. A very basic example is to take a string (like on a guitar, violin, etc.) and pluck it. That is the basic fundamental pitch. If you cut that string in half (either by holding it down or literally cutting it), the pitch will now be twice as high (one octave). Other basic fractions of the string will yield different pitches (2/3 the length of the string is a perfect 5th, etc).

Quick side-note #1: if you’d like to know more about intervals in music, check out this post from Master Claset’s Theory Corner!

Additionally (and more practically to our synth studies), harmonics also serve the function of creating different tones and timbres for different instruments.

One of the core elements of this is something called the Harmonic Series, which is shown in the following image:

Knowing exactly what the picture above means isn’t crucial. What I want everyone to take away from this is to imagine that each note can act like a light switch. The bottom note (lower left corner) is always on. That’s the basis of a pitch itself. By turning the other “light switches” on and off, you will generate different tones and timbres. One combination of switches might create a piano tone while another combination might create a trumpet.

In short, different combinations of harmonics yield different sounds. With those ideas in mind, we can get back to the waveforms!

Since we’ve largely been using Moog Synthesizers as a basis for our discussion, I figured I’d refer to my Minimoog Voyager Manual for a brief description of each primary waveform as Moog provides such a concise description of each:

Sawtooth: “The sawtooth wave is the richest sounding of the four waves. It contains all of the harmonics, and has a bright, buzzy sound. Sawtooth waves are ideal for brass and string sounds, bass sounds and rich accompaniments.”

Square: “The square wave possesses a hollow sound compared to the sawtooth, owing to the fact that it contains only odd harmonics. This hollow characteristic is ideal for distinctive lead and sustained (pad) sounds.?An interesting aspect of the square wave is that the waveshape can be changed to make the top and bottom parts asymmetrical, creating a pulse wave. By changing the shape of the wave, new harmonics are introduced. Pulse waves are ideal for creating clavinet-like sounds, but are also useful for creating lush pads.”

Quick side-note #2: When Moog refers to changing the shape of a square wave and creating “pulse waves,” these are also known as rectangle waves because you are “crushing” the square shape (see imagine above) into a rectangle.

Triangle: “Like the square wave, the triangle wave only contains odd harmonics, but the levels of the harmonics in a triangle wave are much less. The triangle wave has a soft, slightly buzzy sound that is suitable for high- pitched leads (like a flute) or adding a beefy sub-bass to bass sounds.”

Sine: “The sine wave is the purest waveform of them all. It has no harmonics, so it produces a very pure tone. Because of this, sine waves generally aren’t used as primary audio signals, but are often used to reinforce or enhance other waves. They are also used as modulation sources.”

Quick side-note #3: The Minimoog Voyager I will be using for examples doesn’t make a pure sine wave via its oscillators. I can create one using another means, which I will demonstrate but will save the explanation of that section of the Voyager for another day.

To close today, all of these visual and text descriptions are great but hearing an actual example of these waveforms would be equally if not more helpful. In this video, I’ll have one oscillator on and will cycle through the basic waveforms. The Minimoog Voyager is quite interesting and versatile in that it can “blend” between waveforms, so I’ll move the knob slowly, so you can hear the transformation from one type to another and will pause on each pure waveform. Lastly, I’ll create a pure sine wave via another means (per “Quick side-note #3”).

With our oscillators oscillating and our waveforms morphing, we can prepare ourselves for the world of filters and envelopes!